Hi,
You only need to show proof of physical presence in the US of at least 5 years. Two of those years have to be after you turned 14 years old.
You can use your current passport since it has a stamp from immigration showing when you left the US. If you have any old passports, use that as well. You can most definitely use school transcripts. High school or college transcripts can work. If your parents or guardians filed taxes, they probably claimed you as a dependent so you could use those as well. You can also use your own tax records if you have any.
Yes, I was staying with my wife and I was with her for close to two years before she gave birth.
Are you a Nigerian citizen as well? If you are, you should get or have a Nigerian passport. If you do have a Nigerian passport, you don't need a Nigerian visa. If you don't have a Nigerian passport, you should work on extending your Nigerian visa ASAP. These should be your priority because you don't want to be in a situation where you are deported in the lead up to your CRBA appointment and separated from your child. I'm not saying it'll happen but the possibility is there.
I can't say how easy it'll be to extend a visa if you aren't a Nigerian citizen but Nigerian immigration is notorious for being difficult so you'll want to get started on it ASAP. Apply for your baby's CRBA while you're working on your Nigerian immigration status so you kill two birds with one stone.